Application of the Snowmelt Runoff Model to Projecting Climate Change Impacts
on Flow in the Upper Athabasca River Basin
By
Kyle Alexander Siemens B.Sc. University of Victoria, 2014
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE in the Department of Geography
© Kyle Alexander Siemens 2019 University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author.
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Supervisory Committee
Application of the Snowmelt Runoff Model to Projecting Climate Change Impacts
on Flow in the Upper Athabasca River Basin
By
Kyle Alexander Siemens B.Sc. University of Victoria, 2014
Supervisory Committee
Dr. Terry D. Prowse (Department of Geography) Supervisor
Dr. Yonas B. Dibike (Department of Geography) Departmental Member
iii Abstract
Supervisory Committee
Dr. Terry D. Prowse (Department of Geography) Supervisor
Dr. Yonas B. Dibike (Department of Geography) Departmental Member
The projected rise in global temperatures will shift runoff patterns of snowmelt dominated basins, resulting in earlier spring peak flows and reduced summer runoff. Projections of future runoff are beneficial in preparing for climate change induced changes in streamflow, which may necessitate the construction of additional artificial reservoirs to compensate for the reduced natural storage in the form of snow. In this study, the Snowmelt Runoff Model (SRM) was applied to projecting future runoff in the Upper Athabasca River after assessing its ability to simulate historical flows in the basin. SRM utilizes the data-light degree day approach to modelling snowmelt, assuming melt to be proportional to the temperature above freezing through the degree day factor (DDF). Nevertheless, the model performed very well in
simulating flows over both the calibration (2000-2002) and validation (2003-2010) periods. The inclusion of a separate DDF for glaciated areas was found to be essential in accurately
simulating over multiple years with varying snow conditions. The increased melt rate of glacial ice due to its lower albedo relative to snow could explain most of the elevation dependence of the DDF. The SRM with glacier component was applied with four future (2070-2080) climate change scenarios representing uncertainty in climate change projections over the basin. The results show a consistent pattern of change in runoff across all scenarios, with substantial
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increases in May runoff, minor increases over the winter months, and decreased runoff in summer months (June-August). Projected flows are consistent with past modelling studies for the region and with historical trends. In general, the SRM performed very well in simulating historical flows and provides useful runoff projections despite the relative simplicity and few input variables of the model.
v Table of Contents
Supervisory Committee ... ii
Abstract ... iii
Table of Contents ... v
List of Figures ... vii
List of Tables ... viii
1 Chapter 1: Introduction ... 1
1.1 Background ... 1
1.2 Thesis Objectives ... 3
1.3 Thesis Structure ... 3
2 Chapter 2: Literature Review ... 5
2.1 Introduction ... 5
2.2 Snow in the Hydrological System ... 5
2.3 Modelling Approaches ... 7
2.3.1 Energy Balance Models ... 7
2.3.2 Degree-Day Models... 11
2.3.3 Emergence of the Snowmelt Runoff Model (SRM) ... 14
2.3.4 Remote Sensing of Snow Cover ... 16
2.4 Review of the Application of SRM ... 19
2.4.1 Short-Term Forecasting and Climate Change Scenarios ... 20
2.5 Advantages and Disadvantages of Using SRM ... 22
2.6 Summary ... 25
References ... 26
3 Chapter 3: Snowmelt Runoff Modelling for the Upper Athabasca River ... 31
Abstract ... 31
3.1 Introduction ... 32
3.2 Study Area and Data ... 36
3.2.1 Study Area Description ... 36
3.2.2 Data sets ... 38
3.3 Methods ... 40
3.3.1 Markov Chain Monte Carlo (MCMC) methods ... 47
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3.4 Results and Discussion ... 50
3.4.1 Model Performance ... 50
3.4.2 Parameter Distributions and Sensitivity ... 55
3.4.3 Model Bias ... 57
3.4.4 Interannual Variability and the Importance of the Glacial DDF ... 60
3.5 Conclusions ... 64
References ... 66
4 Chapter 4: Projecting Runoff in the Upper Athabasca River for a Warming Climate ... 69
Abstract ... 69
4.1 Introduction ... 70
4.2 The Study Area ... 73
4.3 Data Used ... 74
4.3.1 Hydro-Climate Data ... 74
4.3.2 Remote Sensing Data ... 75
4.4 Methods ... 76
4.4.1 Model Description ... 76
4.4.2 Model Calibration ... 79
4.4.3 Simulation of Future Climate ... 79
4.5 Results ... 82
4.5.1 Snow Cover Area ... 82
4.5.2 Runoff ... 85 4.5.3 Parameter Uncertainty ... 88 4.6 Conclusion ... 90 References ... 92 5 Chapter 5: Conclusions ... 94 References ... 98
vii List of Figures
Figure 1: Location of Study Area (outlined in red) ... 37
Figure 2: Example snow cover map for the study area ... 40
Figure 3: Snow cover fraction with melt season increases removed for the year 2000 (all elevation zones) ... 42
Figure 4: Hypsometric curve for study area with elevation bands ... 44
Figure 5: Calibration vs validation model fit for various approaches to the DDF ... 52
Figure 6: Simulated runoff for 2000-2010 using the monthly DDF approach without a separate DDF for glaciated areas ... 53
Figure 7: Simulated runoff for 2000-2010 using the monthly DDF approach with a separate DDF for glaciated areas ... 54
Figure 8: Posterior distributions of model parameters for monthly DDF with glacier approach. Critical temperature (Tsn), snowmelt runoff coefficient (Cs), rainfall runoff coefficient (Cr), recession coefficient parameters (x and y), date of snowpack ripeness in days since start of calendar year (Ripe Date), the DDF over the November-March (DDF Winter), and DDF for individual months from April through to October. ... 55
Figure 9: Cumulative model error averaged over calibration and validation periods for the monthly DDF model with separate glacier DDF ... 58
Figure 10: Recession coefficient at 300 m3/s (close to the median annual discharge) from all parameter sets when calibrating one year at a time for the monthly DDF approach with no glacier for 2000-2002, using the biweekly DDF approach for 2002, using all three calibration years for the monthly no glacier approach, and using all three calibration years for the monthly with glacier DDF approach. The red lines represent the median parameter values, with the blue boxes spanning from the 25th to 75th percentiles. Red plus signs show outliers (>2.7 standard deviations from median), with the whiskers showing the most extreme parameter values not considered outliers. ... 62
Figure 11: Location of Study Area (outlined in red) ... 73
Figure 12: Hypsometric curve for study area with elevation bands ... 78
Figure 13: Snow cover depletion curves for each elevation zone and climate scenario for 2001. ... 83
Figure 14: Snow cover fraction projections for 2070-2080 for each elevation band ... 84
Figure 15: Mean monthly discharge for baseline (2000-2010) climate and four 2070-2080 climate change scenarios (top), and difference in monthly discharge between the future and baseline climate (bottom) ... 86
Figure 16: Cumulative probability density function for change in Mean Annual Discharge between baseline climate and the four future climate change scenarios for all parameter sets ... 89
viii List of Tables
Table 1: List of parameters determined by calibration. Multiple DDF values were calibrated for various model setups as described in Results section, (e.g. separate monthly DDF values, separate DDF values for snow vs glacial ice). ... 47 Table 2: Calibration (2000-2002) and Validation (2003-2010) period NSE values for various DDF
approaches ... 50 Table 3: Model Fit (NSE) for individual calibration years and averaged over the validation period for various DDF approaches, comparing calibration using a single year with calibration using the whole 2000-2002 calibration period. ... 63 Table 4: Temperature and precipitation changes for future climate scenarios ... 75 Table 5: Glacier area (as calculated from MODIS SCA minimum) and projected percentage change in glacier area for each elevation band ... 82
1 1 Chapter 1: Introduction
1.1 Background
Water resources have been vital to human populations throughout history, utilized for drinking water, irrigation of crops, hydropower production, and industrial use. Despite its abundance on the earths surface, the availability of fresh water is spatially and temporally variable. Many populations in arid and semi-arid regions rely on runoff originating from nearby humid mountainous regions for their water supply (Shen and Chen, 2010). For most regions north of 45°N and at high elevation at lower latitudes, this runoff is dominated by snowmelt (Barnett et al., 2005). The winter snowpack acts as a natural reservoir, storing winter precipitation and releasing it over the spring and summer. With the seasonal distribution of runoff largely governed by temperature in snowmelt dominated regions (Adam et al., 2009), a warming climate will reduce this natural storage capacity, resulting in earlier peak flows in spring and lower flow in summer. This shift is problematic given water use for irrigation and municipal water withdrawals peaks in summer (Schindler and Donahue, 2006). Regions which rely on a deep winter snowpack to maintain summer water supplies may have to construct artificial reservoirs to compensate for this loss of natural storage.
The Canadian Prairies are one such semi-arid landscape, reliant on surface runoff and ground water originating from the snowmelt dominated Canadian Rocky Mountains. Water withdrawal on the Canadian Prairies primarily utilizes surface water, unlike the Great Plains of the United States which extensively exploit groundwater (Gan, 2000). Nearly 50% of water withdrawals on the Prairies have historically been used for irrigation (Gan, 2000). Water is also withdrawn for
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municipal and industrial use, with the oil sands industry on the Athabasca River being a notable consumer. Observed streamflow data shows the shift towards earlier spring freshet, and lower summer flows have been occurring throughout the Rocky Mountains over the past century (Rood et al., 2008, Bawden et al., 2014) corresponding to observed increases in temperature (O’Neil et al., 2016a). Climate models project continued warming for the region, with a 1.5-2.5°C increase in average daily maximum and a 3°C increase in average daily minimum temperatures for 2041-2070 relative to 1971-2000 (O’Neil et al., 2016b).
Modelling runoff provides useful information on the future availability of water which can be used in the management of water resources. Modelling runoff in basins where snow is present requires quantifying the accumulation and depletion of the snowpack. Hydrological models take different approaches to handling these processes. Two of the common approaches utilized in quantifying snowmelt are the energy balance and degree-day methods. While the physically based energy balance approach provides a more accurate calculation of melt given all the necessary data, the relatively high data requirements with very limited observed data often results in estimating most model inputs (Day, 2009). Wherever observed data is sparse, the error introduced from interpolating meteorological variables to the site of interest nullifies the accuracy advantage of using an energy balance model in the first place. In contrast, the degree day method requires only temperature as an input, taking advantage of the high correlation between melt and air temperature (Hock, 2003). Temperature is relatively easy to observe and interpolate, and the simplicity of the degree day method makes it a common choice in many hydrological models (e.g. HBV, SRM, UBC). In addition to the rate of melt, hydrological models must quantify the amount of snow available for melt. This is commonly done through modelling
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the accumulation of the snowpack using meteorological variables (Hock, 2005); however, the Snowmelt Runoff Model (SRM) achieves this by using satellite imagery of snow cover. Given the challenges of interpolating meteorological variables such as precipitation and modelling snow redistribution, the use of snow cover imagery is advantageous in reducing error in snow cover area. SRM uses the degree day method of calculating snowmelt, resulting in a simplistic but versatile model built on three input variables which are widely available (temperature,
precipitation, remote sensed snow-cover). Therefore, the study reported in this thesis utilizes SRM to model the historical and future runoff in the Upper Athabasca River.
1.2 Thesis Objectives
The primary objectives of this thesis are to:
(1) Assess the ability of the Snowmelt Runoff Model to accurately capture runoff for the Upper Athabasca River
(2) Utilize SRM in assessing the effects of climate change on the seasonal distribution of runoff for the Upper Athabasca River
1.3 Thesis Structure
Chapter 1 provides an introduction to this thesis. Chapter 2 provides a literature review of the history of modelling snowmelt runoff, including both physically-based modelling of the energy balance of the snowpack and the development of empirical degree day models as a simplified calculation of melt. Chapters 3 and 4 are stand alone manuscripts utilizing the Snowmelt Runoff Model (SRM) to simulate discharge in the Upper Athabasca River Basin. Chapter 3 presents the calibration and validation of the model using historical data (2000-2010), while Chapter 4 applies the model to simulating future runoff in the basin for multiple climate change scenarios.
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As these chapters are formatted as manuscripts, there may be some repetition in material between chapters. Chapter 5 summarizes the results of this study and provides
5 2 Chapter 2: Literature Review
2.1 Introduction
This chapter will provide an overview on snowpack development and melt processes including the development of energy balance modelling. It will also describe the development of the degree-day method as an alternative to energy balance models, leading into the development of Snowmelt Runoff Model (SRM) and the incorporation of remote sensing into snowmelt modelling. SRM was developed specifically for snowmelt dominated basins, and its
development follows directly from early research correlating temperature with runoff. The chapter concludes with an assessment of the reported advantages and disadvantages of SRM. 2.2 Snow in the Hydrological System
In cold regions, the winter snowpack acts as a natural reservoir, storing precipitation through the winter and releasing it during the warmer months. There is a general trend towards increasing snowfall and duration of snow cover with increasing latitude and elevation, and snow cover may persist year-round at higher elevations. High altitudes may also experience tundra conditions which grade into coniferous forest at lower elevations. Snow cover may be highly unevenly distributed due to winds and slides. The redistribution of snow by winds and the spatially heterogenous rate of snowmelt caused by topography results in substantial variability in the spatial distribution and duration of snow cover.
Freshly fallen snow averages around 10% of the density of water in sub-humid environments, and around 8.3% in cold, dry environments. Once fallen, snow quickly undergoes a
metamorphism which reduces snow crystal surface area, and the snow increases in density to 14-16% that of water (Bruce and Clark, 1966). Several processes contribute to compacting the
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snow and creating a coarser structure, including settling due to gravity and compaction from wind. Until the snowpack becomes isothermal (at the melting point throughout its depth), melt at the snow surface will refreeze within the snowpack. This refreezing of water within the snowpack will increase the size of ice crystals and release latent heat, contributing to the compaction and warming of the snow. Rain on snow events also contribute heat both directly through the heat content of the rain and through the latent heat release from freezing within the snow. This metamorphism is associated with an increase in strength of the bonds between ice grains. Repeated freeze-thaw cycles combined with fresh snowfalls results in a complicated snow structure with numerous ice layers.
Energy input into the snowpack will raise the temperature of the snow. Once the snowpack is ripe (isothermal), additional energy input produces meltwater which is released into the ground. The energy input into the snow includes incoming and reflected shortwave radiation, incoming and emitted longwave radiation, sensible and latent heat fluxes, heat flux from rain, and conduction from the ground below the snowpack. Energy balance models quantify all these energy fluxes for melt calculations (see Eqn. 1). Incoming shortwave (solar) radiation varies temporally with season and time of day, as well as spatially with latitude and local topography. Reflected solar radiation (outgoing shortwave) varies with the albedo of the material, with fresh snow reflecting up to 90% of incident radiation. Incoming longwave radiation primarily
originates from the atmosphere and can be approximated using air temperature and pressure. Snow emits radiation (outgoing longwave) in accordance with its temperature. The sensible heat flux refers to conduction between the snow surface and the atmosphere, and is proportional to the temperature gradient between the two. Similarly, the latent heat flux
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results from a vapor pressure gradient, with a positive vapour pressure gradient resulting in condensation and energy release, while a negative vapour pressure gradient will result in energy loss to evaporation. Rain falling and freezing on snow will release latent heat, thereby warming the snowpack. If the rain does not freeze, the energy released into the snowpack will be equal to the difference between the initial energy in the water droplet and its energy after coming to thermal equilibrium within the snow. Finally, the energy transfer due to conduction from the ground at the base of the snowpack is proportional to the temperature gradient at the snow base.
Melt water movement from the snow surface to the ground can be slow, ranging from two to sixty centimetres per minute (Gray and Male, 1981). While initially ice layers in the snow inhibit the vertical drainage of water, within a few hours drainage channels develop allowing water to quickly travel vertically through these ice layers. Upon reaching the snowpack base meltwater will percolate into the ground or flow along the surface once the ground becomes saturated. The time taken for meltwater to percolate through the snowpack, move downhill as sub-surface or sub-surface flow to a stream, and flow through the stream to the point of interest, all contribute to the total lag time between the time of melt and the time water appears at a gauging location.
2.3 Modelling Approaches 2.3.1 Energy Balance Models
For the many regions of the world where runoff is dominated by snowmelt, it is important to accurately quantify the amount and timing of snowmelt for flood prediction and
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resource management. Melt models can be divided into two primary types: energy-balance models and degree-day models, with a gradient of intermediary forms in between. Energy-balance models seek to evaluate the various fluxes contributing to melt for a more physically based computation of melt, while degree-day models utilize only temperature. Despite their simplicity, degree-day models can provide an accurate calculation of melt in locations which may lack the data required for the energy balance method.
Ahlmann (1935) derived the first empirical formula for the computation of ablation in the 1920s using incident radiation, air temperature, and wind velocity (Hock, 2005). Svedrup (1935) studied ablation on Isachsen’s Plateau, performing an energy balance to determine the relative contributions of energy balance components to ablation. For the period of June 26th to August
15th, the total ablation was calculated to be 42.5 cm, compared to the measured ablation of
41.5 cm. It was calculated that radiation caused 56% of the total ablation, conduction from the air caused 29.4%, and condensation of water vapor caused 14.7%. Evaporation caused 3.5% of ablation. At another location near sea level, only 24% of ablation was calculated as being caused by radiation. This energy balance took the same form used in most energy balance studies since, and as presented by the US Corp of Engineers (1956) and Hock (2005) in their reviews of melt modelling:
𝐻𝑁+ 𝐻𝐻+ 𝐻𝐿+ 𝐻𝐺 + 𝐻𝑅 + 𝐻𝑀 = 0 (1)
Equation 1 shows the sum of net radiation (𝐻𝑁), the sensible heat flux (𝐻𝐻), the latent heat flux
(𝐻𝐿), the ground heat flux (𝐻𝐺), the heat flux due to rain (𝐻𝑅), and the energy consumed by
melt (𝐻𝑀) is zero. The net radiation includes incoming solar radiation (insolation) minus
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fluxes, 𝐻𝐻 and 𝐻𝐿, were calculated using the gradient flux method, setting the flux proportional
to the potential temperature gradient in the case of sensible heat and the specific humidity gradient in the case of latent heat. Svedrup (1935) was the first to apply the now commonly used gradient flux method to snow or ice (Hock, 2005). By convention, fluxes directed toward the snow or ice surface are positive. If snow is subfreezing, heat is required to bring its
temperature up to the melting point before melt can begin. Melt can then be computed from the energy available for melt:
𝑀 = 𝐻𝑀
𝜌𝑤𝐿𝑓 (2)
Here 𝑀 is the melt depth, 𝜌𝑤 is the density of water, and 𝐿𝑓 is the latent heat of fusion.
A detailed overview of energy-balance modelling for a snow surface is given by the Corp of Engineers (1956). The relative importance of the different energy-balance components varies with location: solar radiation may be more important in open terrain, but of less importance in forested areas and decreases in importance at higher latitudes. Because of the varying
importance of different energy-balance components, there is no universally applicable index for snowmelt. The net heat flux is normally positive during the day and negative at night during the melt season. This often results in a snow crust as free liquid water in the top layers of the snowpack refreeze at night.
Clouds cause substantial variation in insolation values, but their effects are difficult to calculate. Slope also affects the intensity of insolation, with south (north) facing slopes receiving more insolation than north (south) facing slopes in the northern (southern) hemisphere. Tree
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varying depending on the forest characteristics. Snow albedo varies considerably, with newly fallen snow reflecting around 80% of insolation, while older snow may reflect only 40%. Because snow is translucent, insolation is not only absorbed at the surface but penetrates to some depth in the snowpack. Snow is a near perfect blackbody in the case of longwave radiation, and so emits and absorbs radiation in accordance with the Stefan-Boltzmann law. Back radiation emitted by the earth’s atmosphere, clouds, and trees also contributes to snowmelt (Corp of Engineers, 1956).
Calculation of snowmelt on a basin-wide scale is complicated even more by the spatial and temporal variability of the fluxes across the snow surface (Ferguson, 1999). Calculating the sensible heat flux requires air pressure, snow surface temperature, air temperature (which can have highly variable lapse rate), and wind speed (which varies with local topography). Net radiation depends on cloud cover, albedo, and shading effects from topography, which can be accounted for by using a digital elevation model (DEM). The data required to use such full energy balance method are often not available in most remote regions where it often needs to be applied (Day, 2009). Moreover, difficulties in extrapolating the numerous variables required for an energy balance model raises concern in the accuracy of distributed energy-balance models (Ferguson, 1999). While there are a few physically based snow models (e.g., CROCUS, SNTHERM, DAISY) (Hock, 2005), the data intensive nature of energy balance modelling and the difficulty in forecasting meteorological variables reduces the predictive ability of these models. These issues lead to the use of the degree-day model as an alternative method of calculating melt with less intensive data requirements.
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2.3.2 Degree-Day Models
Degree-day models assume an empirical relationship between temperature and snow or ice melt. The close relationship between air temperature and melt rates was first described by Finsterwalder and Schunk (1887) and has since been refined and widely applied (Hock, 2003). Leach et al. (1933) compared plots of air temperature and runoff during a period of positive temperatures following a snow storm, noting high correlation between above freezing temperature and melt. Collins (1934) sought to utilize the degree day method in predicting water supply for Coeur d’Alene Lake, a storage reservoir in northern Idaho used for several hydroelectric projects. Below freezing temperatures were identified as having no effect on runoff, while above freezing temperatures correlated to melt, percolation, and evaporation. The study attempted to find a relation between positive degree days and runoff using data from three weather stations in the region. Multiple elevation bands were used with
temperature interpolated to each band. Total accumulated degree days were weighted by the area of each band, then plotted against accumulated runoff as measured from USGS stream gauging stations. Accumulated runoff initially increased steeply and steadily with accumulated degree days before levelling off. A similar ‘S’ curve was produced by Wilson (1941), another study which plotted accumulated degree days against accumulated runoff. Rango and Martinec (1995) later noted the failure to account for snow cover area or runoff losses by the Collins (1934) study as the reason for the ‘S’ curve, with the first 500 degree days accounting for 85 percent of runoff.
Linsley (1943) outlines methods developed by the Weather Bureau office in Sacramento for forecasting discharge in the Sacramento and San Joaquin River basins in California. The
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importance of determining the contribution of snowmelt to river discharge was noted, along with the usefulness of the degree-day model in determining melt given the lack of
meteorological data for many regions beyond temperature and precipitation. Similar to Collins (1934), the elevation dependence of temperature was accounted for through the use of
elevation bands. Degree day values were multiplied by the degree day factor (DDF) to give total melt over the basin. One potential method of determining the DDF is presented as dividing total runoff by accumulated degree days over a brief period during which there is little or no rain. The increase in the DDF throughout the melt season was noted, which was attributed to the ripening of the snowpack and variations in radiation or other melt factors. Rango and Martinec (1995) commented on the large seasonal increase in the degree day factor found by Linsley (1943), from 0.1 cm/°C/day to 0.7 cm/°C/day, as the result of flow recession not being taken into account (not all of the snowmelt appears immediately as runoff), in addition to the natural seasonal increase in the DDF.
Since these early studies related accumulated temperature directly to runoff, their approach ignored the depletion of the snowpack, runoff routing, and other hydrological processes. As in Linsley (1943), modern usage of the degree-day method also relates degree days to melt depth. However, the various models take different approaches in transforming calculated melt into runoff. The general form of the degree-day method is:
𝑀 = 𝑘(𝑇𝑎− 𝑇𝑏), 𝑇𝑎 > 𝑇𝑏 (3)
Where 𝑀 is the melt depth, 𝑘 is the degree day factor, 𝑇𝑎 is the air temperature, and 𝑇𝑏 is the
reference temperature, usually 0°C. This method continues to be widely used because of the wide availability and relative ease of interpolating/forecasting air temperature; and strong
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accuracy despite the simplicity of the relation (Hock, 2003; US Corp of Engineers, 1956). The high correlation between air temperature and other energy balance components make air temperature a useful index for calculating melt (Day, 2009). The degree-day method is
especially effective in forested areas due to the reduced importance of insolation (U.S. Corp of Engineers, 1956). The method can produce comparable results to an energy balance model if applied correctly; the DDF must be adjusted through the melt season to account for its seasonal increase due to lower albedo and higher insolation (Rango and Martinec, 1995). The DDF is spatially and temporally variable, varying with local albedo, shading, slope and aspect, among other factors. Despite this variability, the degree-day method performs well in hydrological models, in part because of the smoothed response of runoff that provides some forgiveness to day to day errors in melt depth (Rango and Martinec, 1995).
The variability of the degree day factor and the fact that melt is influenced by many variables other than temperature has led to the formulation of enhanced degree-day models. Enhanced degree-day models often include net radiation or net shortwave radiation, given its importance to the energy budget of a snow surface. These models often assume the form:
𝑀 = 𝑘𝑇 + 𝑎𝑅 (4)
Where 𝑅 is the net radiation and 𝑎 is a coefficient accounting for the contribution of radiation to melt. This approach has been applied in hydrological models including SRM, often yielding improved results over the base degree-day model (Hock, 2003).
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2.3.3 Emergence of the Snowmelt Runoff Model (SRM)
Martinec (1960) found good correlation between the DDF and snow density and proposed a linear relationship between the two variables. Martinec (1963) expanded on this by attempting to model basin-wide snowmelt. Measured temperature was extrapolated to the mean
elevation of the basin and used to calculate degree days. A lag time of 4 hours was determined using the observed lag between the rise in temperature and the rise in discharge. The recession in runoff was computed using:
𝑄 = 𝑄0𝑒−𝑘𝑡 (5)
Where 𝑄 is the discharge after time 𝑡, 𝑘 is a coefficient representing the rate of flow recession, and 𝑄0 is the initial discharge. Daily runoff was then computed by applying the degree day
method to calculate melt and adding the contributions from rain and recession flow from the previous day. This process of calculating snowmelt runoff was formally expressed by Martinec (1965):
𝑄𝑛 = 𝑐[𝑎𝑛𝑇(1 − 𝑘) + 𝑄𝑛−1𝑘] (6)
Where 𝑐 is the runoff coefficient, 𝑇 is the number of degree days, 𝑎 is the degree day factor, 𝑘 is the recession coefficient from equation (5), and 𝑛 is an index expressed in days. This
formulation was extended in Martinec (1970). The basin was divided into elevation bands with melt calculated separately for each band to account for differences in temperature and snow cover area with elevation. These changes brought the model near the form in which it was formally introduced as the Snowmelt Runoff Model by Martinec (1975), which introduced a recession coefficient which varied with discharge to account for increased basin responsiveness at higher flows. Martinec (1975) also added rainfall to the melt depth before applying the
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recession coefficient to calculate runoff. The present form of the model includes separate runoff coefficients for snowmelt and rainfall:
𝑄𝑛 = ∑(𝑐𝑆𝑖𝑛𝑎𝑖𝑛𝑇𝑖𝑛𝑆𝐶𝐴𝑖𝑛+ 𝑐𝑅𝑖𝑛𝑃𝑖𝑛𝑅𝐶𝐴𝑖𝑛)
𝑖
(1 − 𝑘(𝑥, 𝑦)𝑛) + 𝑄𝑛−1𝑘(𝑥, 𝑦)𝑛 (7)
The discharge, 𝑄, is calculated from the individual contributions of snowmelt, rainfall and recession from the previous day discharge. The temperature 𝑇 is adjusted via a lapse rate to the hypsometric mean elevation of each elevation band. Temperature is multiplied by the degree day factor 𝑎 to get depth of melt, and this is multiplied by the snow cover area 𝑆𝐶𝐴. The contribution of precipitation is calculated by multiplying the precipitation depth 𝑃 by the rainfall contributing area 𝑅𝐶𝐴. The runoff coefficients 𝑐𝑆 and 𝑐𝑅 correspond to the ratio of snowmelt and rainfall to runoff, respectively, and account for losses such as evaporation and sublimation. It is recommended that if the study basin exceeds 500 metres in elevation range that it be divided into bands of about 500 m each to account for varying melt conditions (temperature and precipitation lapse rates). The snowmelt and rainfall contributions are
calculated for each band individually and summed to obtain their total contribution. The index 𝑖 is used to indicate the elevation zone. The sum of the snowmelt and rainfall contributions are then multiplied by the recession coefficient 𝑘, which expresses the decline in discharge during a period with no snowmelt or rainfall. This flow is then added to the recession flow from the previous day. The recession coefficient is a function of parameters 𝑥 and 𝑦, accounting for the nonlinear response of the basin.
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2.3.4 Remote Sensing of Snow Cover
Given the large areas occupied by snow cover, in situ measurements are insufficient for accurate mapping of snow extent. Remote sensing has allowed for the wide scale mapping of snow extent. The use of remote sensing in determining snow covered area began with air photos and has become increasingly practical with the abundance of satellite imagery. As air photos were generally used for topographic surveys, they were usually taken in late spring after snow cover had melted thus dedicated flights had to be flown to acquire snow cover data. The emergence of satellite imagery has provided an alternative for large scale observation and analysis of snow cover. The use of satellite imagery for snow cover analysis began in the 1960s. The first Landsat satellite was launched in 1972 (originally named the Earth Resources
Technology Satellite), providing 90 m resolution at nadir and providing data for mid latitude regions every 18 days (Gray and Male, 1981). Following the launches of Landsat-1 and NOAA-2, deployed the same year, it was proposed that satellite data could be used in determining snow cover area and predicting snowmelt runoff (Rango, 1980). To this end, NASA carried out testing of satellite imagery utilization in operational runoff predictions under the Applications Systems Verification and Transfer (ASVT) program from 1975 to 1979. The use of satellite imagery was found to be valuable in reducing forecast error, with the use of snow cover imagery in SRM reducing flow estimate errors by 10-15% for three basins in California (Rango, 1980). The use of satellites in operational snowmelt forecasting at the time was limited by the long lag time between data acquisition and delivery to the end user, as well as infrequent coverage at acceptable resolutions.
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Snow has distinctive characteristics in the visible, near infrared, and microwave portions of the electromagnetic spectrum that allow for its detection through remotely sensed imagery. Optical imagery can be used to obtain much higher spatial resolution than passive microwave imagery but is limited by hours of daylight and presence of cloud cover. A common approach to detecting snow is to use two spectral bands: one centred in the visible part of the spectrum, and one centred in the near infrared around 1.65 μm. These bands are used for snow identification because while clouds and snow have similar reflectance below 1 μm, their reflectance diverges and achieves a maximum difference in the near infrared (Meier, 1980). Snow cover is typically identified using the Normalized Difference Snow Index (NDSI):
𝑁𝐷𝑆𝐼 = 𝑟𝑣𝑠− 𝑟𝑖𝑟 𝑟𝑣𝑠+ 𝑟𝑖𝑟
(8)
With 𝑟𝑣𝑠 and 𝑟𝑖𝑟 being the visible and shortwave infrared reflectance, respectively. For Landsat,
bands 2 (visible) and 5 (infrared) are used while for Moderate Resolution Imaging Spectrometer (MODIS), band 4 (visible) and 6 (infrared) are used. An NDSI greater than 0.4 is used to indicate snow cover. Additional criteria that the reflectance of the visible band be greater than 0.11 and the reflectance of the infrared band be greater than 0.10 prevent misidentification of water as snow, as water also tends to have high NDSI values. (Rees, 2005)
Snow cover maps have been available since 1966, derived from data from NOAA’s GOES and POES satellites. These weekly charts of the northern hemisphere had a spatial resolution of 190 km (Hall et al., 1996). Since the launch of the NOAA Advanced Very High Resolution Radiometer (NOAA-AVHRR), we have had the ability to observe daily snow cover on a continuous basis at 1.1 km resolution. This resolution is still too coarse for hydrological modelling in smaller basins
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but can be used over larger areas and for climate studies (Rango, 1996). Following the launch of MODIS in 1999, NASA has been producing global daily snow cover maps at 500-meter
resolution using MODIS imagery. An 8-day composite snow cover product is produced from these daily products to minimize cloud cover and obtain the greatest snow cover extent over the 8-day period (Hall et al., 2002).
Most hydrological models (HBV, NWS, UBC, SHE) simulate the growth and decay of the
snowpack (Hock, 2005), whereas SRM takes advantage of satellite imagery in determining snow cover area. Temperature is used in those models to determine whether precipitation falls as rain or snow. Meteorological stations are sparse in high elevation regions (EDW Working Group, 2015), and it is necessary to extrapolate temperature and precipitation across the study basin to simulate snowpack. Temperature and precipitation are also spatially variable and should be adjusted with elevation using temperature and precipitation lapse rates. Despite temporal and spatial variations in temperature lapse rates, most models use a fixed lapse rate, which can introduce large errors in temperature for basins with a large elevation range (Blöschl, 1991). Precipitation can be highly localized and most gauges systematically under catch snow,
particularly in windy conditions, which can be problematic for models which model the growth of the snowpack (Ferguson, 1999). A model can accurately calculate melt rates but still give poor runoff estimates if there is error in the snow cover area. Thus models that model
snowpack growth can give erroneous results not through a fault in the model itself, but through uncertainty in meteorological variables leading to inaccurate snow cover area. SRM reduces the error involved in modelling snowpack growth by using satellite imagery to determine actual
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snow cover. However, when used in forecast mode, SRM must rely on snow cover data from previous years to extrapolate SCA into the future.
2.4 Review of the Application of SRM
SRM has been applied to over 100 basins, ranging in size from 0.76 to 917,444 km2 (Martinec et
al., 2008). Initially applied to small European basins, the model has since been applied to snow covered regions worldwide. A list of basins where SRM is used is provided by Martinec et al. (2008). SRM has been used in many of the mountainous regions of Europe, Canada, and the USA. In the southern hemisphere it has been applied in several basins within the Andes, as well as in New Zealand and Australia. It has also been used in various locations throughout the Himalayas, China, and Japan. SRM has recently begun being applied in northwestern China, where its limited meteorological data requirements are advantageous given the sparsity of hydro-meteorological data in the region (Abudu et al., 2012).
Various enhancements to SRM have been tested since its introduction. The addition of a radiation component to the melt calculation is a common enhancement for improving model performance (e.g. Brubaker et al., 1996; Li and Williams, 2008; Vafakhah et al., 2014). These studies often divide their study basins into aspect zones as well as elevation zones to account for spatial variations in received insolation. Alternatively, Abudu et al. (2016) applied set temperature adjustments to different aspect and slope classes to account for topographic effects on melt without explicitly modelling radiation. Harshburger et al. (2010, 2012) used an enhanced version of SRM which incorporates an antecedent temperature index method to track the ripeness of the snowpack and minimum and maximum critical temperatures to
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partition precipitation into rain, snow, and a rain snow mix. Both enhancements improved model performance.
2.4.1 Short-Term Forecasting and Climate Change Scenarios
SRM has been applied to both short term forecasting and climate change studies. Short-term runoff forecasts utilizing SRM have been shown to be useful up to a six-day lead time (Nagler et al., 2008) with forecast skill declining with lead time (Harshburger et al., 2010). This reduced forecast skill can be at least partially attributed to error in weather forecasts. Temperature and precipitation from short term forecasts or climate change projections is used as model input, leaving only snow cover area to be determined. SRM can extrapolate SCA using Modified Depletion Curve (MDC). An MDC is produced by creating a relationship between SCA and cumulative snowmelt depth using historical data. A family of MDCs can be produced from multiple years of historical data. To extrapolate melt, an MDC with similar snow conditions to the study period is selected, and SCA is extrapolated using the MDC to determine what SCA is associated with the forecasted cumulative melt depth.
SRM includes a built-in climate-scenario module to simulate year-round stream flow under a changed climate (Martinec et al., 2008). Rango and Martinec (1997) quantified the seasonal shift in runoff due to warmer temperature for the Rio Grande basin in Colorado. A wet year, dry year, and average year were utilized in creating MDCs, which were used to simulate the effects of a 4°C temperature increase. Precipitation was assumed to remain the same thus annual runoff remained little changed, but there was a shift toward increased winter runoff at the expense of summer runoff. Seidel et al. (2000) apply SRM to the Ganges and Brahmaputra
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basins, and simulate runoff under a temperature increase of 1.5°C and a 10% increase in precipitation. These are the largest basins in which SRM has been applied, at 917,444 km2 and
547,346 km2, respectively. The simulated climatic changes were found to increase peak runoff
during flooding by 20% for the Ganges and 30% for the Brahmaputra, while April-December runoff volume increased by 25% for both basins. Seidel et al. (2008) simulated the effects of climate change on the 3250 km2 Rhine-Felsberg basin in the Swiss Alps, finding more summer
flooding events as summer snowfalls were replaced by rain.
Despite the MDC methodology for estimating future snow cover developed for SRM, several studies opt to instead use a range of prescribed changes to SCA. Ma et al. (2013) utilized
downscaled GCM output to develop multiple climate change scenarios for the Kaidu watershed in northwestern China. These scenarios included keeping SCA the same as the historical climate and evaluating the effects of both increases and decreases in SCA on runoff. Tahir et al. (2011) examined the effects of a changed climate on flow rates in the Hunza River basin in Pakistan. Three climate change scenarios were examined: a temperature increase of 4°C; a 20% increase in cryosphere area until 2075 and 10% increase until 2050, assumed based on increased
precipitation; and a third scenario combining increased temperature with increased cryosphere area. Nolin et al. (2010) examined the effects of climate change on a glacierized basin, assessing multiple prescribed reductions in glacier area.
Few SRM studies have explicitly accounted for glaciers, despite the model’s frequent use in mountainous glacierized basins. Schaper and Seidel (2000) applied separate glacier and snow DDFs in SRM to a climate change study of three basins in Switzerland. Glacier area was reduced for the warming climate based on an equilibrium line shift calculated from the increase in
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summer temperature. Rango et al. (2008) examined the effects of a warmed climate on stream flow in the glaciated Illecillewaet basin in British Columbia. The higher DDF for glacial ice was accounted for using the minimum observed SCA as an estimate of glacier area. For a non-glaciated basin, an increase in temperature would shift peak runoff earlier in the season, while total runoff would remain the same (assuming seasonal snow cover and precipitation remain unchanged). This is not true of a glaciated basin, where there will be increased runoff due to glacial melt. This study did not account for glacial retreat due to increased melt, resulting in overestimated projected runoff. Nolin et al. (2010) apply SRM to a glacierized catchment in the Pacific Northwest. Glacier area was used in place of snow cover area in the traditional SRM setup, with snow cover accounted for through precipitation and temperature. Separate DDFs for snow and ice were utilized.
2.5 Advantages and Disadvantages of Using SRM
The Snowmelt Runoff Model is built around the remote sensing of snow cover and the use of the degree day model. As previously discussed, degree day models have the advantage of requiring only temperature to calculate snow melt while producing results comparable to those of an energy balance model for many hydrological applications. Degree day models have been commonly used throughout the history of snow melt modelling due to the wide availability of temperature data and the relative sparseness of measurements for other meteorological variables which would be required to do a full energy-balance model. Temperature is also relatively easy to interpolate, and degree-day models avoid the error involved in requiring other meteorological variables which may be more difficult to interpolate. The use of
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temperature as the sole index of melt can be problematic, however, as it is one of many factors influencing melt and so the degree-day factor must be varied to account for the changing relative contributions of the various energy-balance components. The degree-day factor gradually increases through the melt season for multiple reasons including increasing insolation, decreasing albedo, and the ripening of the snowpack. The degree-day factor also varies spatially due to the aspect of the snow surface, shading from surrounding topography, and elevational effects on energy-balance components (e.g., temperature decreasing with elevation). For a degree-day model to be applied in hydrological modelling, an average basin-wide DDF must be determined. The ease of forecasting temperature is also an advantage for forecasting streamflow, as other variables are more difficult to forecast.
The sparseness of meteorological data in the high-elevation regions in which SRM is often applied and the difficulty in interpolating this data make the simulation of snow-cover area problematic. Accurate snow-cover area is important for runoff modelling as errors in calculated snowmelt will be proportional to the error in snow-covered area. Models that simulate the snowpack may encounter issues with small-scale processes such as blowing snow, but even if the model were perfect, it may still produce erroneous results due to inaccurate meteorological data. The use of satellite imagery in SRM to determine snow-cover area avoids the uncertainty involved in modelling the snowpack. This approach comes with its own flaws. Infrequent satellite imagery or the presence of cloud cover may prevent the mapping of snow cover for periods of time, and resolution must be sufficiently high to accurately map snow cover for a basin, with smaller basins requiring higher resolution imagery (Day, 2009).
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In a review of several runoff models, Day (2009) noted that while SRM requires less calibration than other models, it should not be applied to basins without historical discharge records to calibrate the model. These parameters include the runoff coefficient, which can be calculated as the long term ratio between precipitation and runoff; lag time, which can be determined by examining the lag between a rise in temperature and a rise in discharge; and the recession coefficient, which can be determined by plotting discharge on for each day against discharge on the following day. While its developers do not consider SRM to be a calibration model and state parameter values should be selected based on hydrological judgements, in practice, parameter values often require adjusting to provide accurate results (Ferguson, 1999). The runoff
coefficients account for losses due to evapotranspiration and are varied temporally to account for changes in losses over time. In practice, these coefficients are often used to correct for systematic errors in modelled runoff (Ferguson, 1999).
SRM takes a minimalist approach to runoff routing and does not explicitly model groundwater. Most runoff models represent flow routing through a series of reservoirs, where outflow from a reservoir is modeled as some function of the volume of water in that reservoir (Ferguson, 1999). Separate reservoirs may be used to represent surface flow, interflow and groundwater. SRM features the simplest representation of runoff routing, using a single non-linear reservoir. The use of a non-linear reservoir allows SRM to capture the increased responsiveness of a basin hydrograph at high flows, but the single reservoir approach lacks the ability to fit the same range of conditions as a model with a more detailed representation of runoff routing.
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2.6 Summary
A substantial portion of the world’s population lives in regions in which streamflow is dominated by snowmelt runoff. As the climate changes and snowpacks shrink, there will be reduced summer flows and increased runoff in the winter and spring. Modelling runoff is important for managing water resources, as shifts in runoff patterns impact irrigation, hydroelectric projects, stream ecology, and industrial and municipal use of water.
Snow accumulates at high latitudes and high elevations through the fall and winter, before being released as meltwater in the spring. Several energy fluxes contribute to the energy balance of the snowpack, with the largest contributors being the radiative and turbulent heat fluxes. Because of the sparseness of observations and difficulty in interpolating or forecasting many of the required variables, temperature-index models are often used instead.
Temperature functions well as the sole index of melt because it is closely correlated with other melt factors such as net radiation.
The remote sensing of snow covered area has allowed for more accurate assessment of snowmelt runoff. Though the Snowmelt Runoff Model was originally developed before
widespread satellite imagery at a resolution useful to runoff modelling, the increased frequency and resolution of satellite imagery has allowed SRM to become a frequently used hydrological model for snow-covered regions. Originally developed for simulating flow for small European basins, SRM has since been applied to basins around the world. The model has been used in conjunction with meteorological forecasts for producing short-term runoff forecasts as well as with GCM output for climate-change impact studies.
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3 Chapter 3: Snowmelt Runoff Modelling for the Upper Athabasca River
Abstract
The Snowmelt Runoff Model (SRM) is a widely used hydrological model for simulating runoff in snowmelt dominated mountainous basins due to its relative simplicity and the accuracy
provided by utilizing remotely sensed snow-cover imagery to determine snow-cover extent, avoiding the error associated with modelling the snowpack. Remotely sensed snow-cover is combined with the temperature-based degree day method for simulating snowmelt, an
advantageous approach in mountainous regions where meteorological observations are sparse and difficult to interpolate. The degree-day method calculates melt by relating the mean daily temperature to melt depth through the degree-day factor (DDF), a coefficient obtained through measurement or calibration. Despite being widely applied in glaciated basins, SRM studies have rarely explicitly accounted for the difference in DDF between glacier ice and snow, instead applying a zonal (elevation dependent) DDF. SRM was calibrated for the Upper Athabasca River Basin with separate snow and ice DDFs, satisfactorily simulating flows over the calibration (2000-2002, average NSE of .93) and validation (2003-2010, average NSE of .88) periods. The glacier DDF model produced comparable results to that of the zonal model. Zonal model calibration produced DDF values consistent with glaciers being the largest drivers of DDF elevation dependence. Accounting for the higher glacier DDF, either explicitly or through elevation dependence, was found to be essential in capturing interannual variability in melt conditions.
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3.1 Introduction
Streamflow forecasts are valuable source of information for water resource management. Runoff predictions can be used to assess water availability for irrigation, hydroelectricity generation, and municipal or industrial use (Ferguson, 1999). For most regions north of 45°N and mountainous regions at lower latitudes, this runoff is primarily derived from snowmelt (Barnett, 2005). In snowmelt dominated regions, changing temperatures are of greater interest to forecasting flow than precipitation, as it is temperature that governs the timing and
magnitude of meltwater (Arnell, 1999). The reduction of the winter snowpack and resulting reduction in summer runoff is of importance to regions such as the Canadian Prairies, where water usage peaks in the summer due to demand for irrigation and municipal water
withdrawals (Schindler and Donahue, 2006). Although climate change is expected to intensify the hydrological cycle, increasing global average precipitation, large regions will experience reductions in precipitation (Arnell, 1999). Changes in seasonal runoff patterns over the last century have been observed in numerous rivers originating in the Rocky Mountains, with an analysis of 14 rivers located throughout the Canadian and Northern USA Rocky Mountains finding an increasing trend in winter flows and a decreasing trend in summer flows (Rood et al., 2008). Quantifying future runoff will assist water consumers in preparing for changing runoff seasonality.
With runoff in the Canadian Rocky Mountains dominated by snowmelt, it is essential that snowpack processes be modelled accurately. Both the accumulation of the winter snowpack and its subsequent release as melt water in the spring must be properly captured, both of which present challenges in mountain environments where meteorological conditions are
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spatially variable and observations can be sparse. Precipitation can be highly localized, leading to difficulties in accurately quantifying basin-wide runoff without a dense network of
precipitation gauges (Faurès et al., 1995). This uncertainty in precipitation will affect both modelled rainfall runoff and modelled snow accumulation. Additional uncertainty in modelling snow accumulation stems from the use of a static temperature threshold to differentiate snow from rain. Identical near-surface air temperatures could result in either rain or snow depending on the local lapse rate, which will vary depending on atmospheric conditions (Feiccabrino et al., 2015). Wind and slides act to redistribute snow once it has fallen, resulting in heterogeneous snow cover. Many hydrological models attempt to simulate the accumulation and distribution of snowfall (e.g. HBV), while others avoid the uncertainty in modelling the snowpack by using remotely sensed snow cover imagery (Ferguson, 1999).
The contribution of melt to runoff can be modelled using the energy-balance or degree-day methods. Energy-balance modelling is a physically based approach in which the various heat fluxes into the snow or ice surface are quantified. This approach is data intensive, requiring vertical temperature and specific humidity gradients, wind speed, shortwave and longwave incoming and outgoing radiation, and precipitation (Hock, 2005). Hence, degree-day models have developed in response to the high data requirements and computational complexity of energy balance models. While net radiation tends to be the largest heat flux, the close
relationship between temperature and other energy-balance components allows temperature to be used as a relatively accurate index for melt estimation. Taking advantage of the high correlation between temperature and melt, degree-day models assume a linear relationship between the two variables (Hock, 2003). The degree-day method is utilized in many
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hydrological models as it can obtain similar accuracy in results to energy-balance models despite its simplicity and light data requirements (Rango and Martinec, 1995).
This degree day – melt relationship, however, varies both temporally and spatially reflecting changing relative contributions of the different energy fluxes. Slope and aspect affect the amount of insolation a given point on the snowpack receives. Tree cover reduces the influence of the turbulent heat fluxes and enhances long wave radiation relative to open terrain (Woo and Giesbrecht, 2000). The degree day factor (DDF), a coefficient relating temperature to melt depth, tends to be larger at higher elevations due to the increased relative contribution of radiation (Hock, 2003). DDF also tend to be higher for glaciers due to the lower albedo of ice relative to snow. These spatial variations in melt conditions may impact the ability of a single basin wide melt factor to accurately model snowmelt runoff. The DDF varies temporally both on a daily timescale and a seasonal timescale, with day-to-day fluctuations due to changing
meteorological conditions. Despite this day-to-day variability, when averaged over several days the DDF is much more consistent, and the smoothed response of runoff to snowmelt events allows some forgiveness to daily errors in melt quantity (Hock, 2003; Martinec et al., 2008). Seasonally, the DDF increases throughout the spring from the increased contribution of
radiation and decreasing albedo of the snowpack. Accounting for these seasonal changes is vital to accurately modelling snowmelt runoff (Rango and Martinec, 1995).
The Snowmelt Runoff Model (SRM) is a conceptual hydrological model for simulating runoff in snowmelt dominated basins. SRM has been applied in over 100 basins worldwide, ranging in size from under 1 km2 to over 900,000 km2 (Martinec et al., 2008). Modelling of snowmelt
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snow accumulation and redistribution; and using a degree-day model rather than a more data intensive energy-balance model. While many other models utilize the degree-day approach, the advantage of SRM is in its incorporation of remotely sensed imagery, reducing error normally associated with modelling the snowpack.This approach results in only three required input variables which are relatively widely available: temperature, precipitation, and snow cover area. SRM is shown to produce satisfactory results despite its simplicity, making it an ideal model for determining streamflow in mountainous regions where data may be lacking (Day, 2009; EDW Working Group, 2015). However, most SRM studies in glacierized basins have not explicitly accounted for separate melt factors for snow and ice, though many use separate DDFs for each elevation band (e.g., Tahir et al., 2011; Ma et al., 2013). Increasing the DDF with
elevation would account for more extensive glacier cover and the higher DDF for snow due to the increased relative contribution of solar radiation to melt (Hock, 2003). This study utilizes SRM in simulating runoff for the Upper Athabasca River Basin at Hinton. The importance of seasonal, elevational, and glacial variations in DDF is examined through comparison of several approaches to handling the DDF. The DDF and other parameters were determined solely through calibration within a range of physically plausible values, testing (validating) the ability of each model approach to realistically simulate the basin hydrograph in the absence of field measurements to inform parameter value selection.
Parameters for SRM are intended to be physically based, with parameter values chosen based on basin characteristics and historical data (Martinec et al., 2008). In practice, the physical basis of these parameters is weak, and some calibration is often necessary to obtain acceptable results. As with all conceptual hydrological models, the simplification and spatial aggregation of
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hydrological processes results in parameters which cannot be directly measured or obtained through theory (Ferguson, 1999; Liu and Gupta, 2007). Instead, models are calibrated by tuning parameters through a range of physically plausible values to maximize model fit. This lack of a definitive, measurable parameter set leads to the concept of equifinality, where many different model structures and parameter sets can produce acceptable representations of the behaviour of a system (Beven and Freer, 2001).
Estimating parameter uncertainty is typically handled using data assimilation (Liu and Gupta, 2007), a general term which refers to mathematical techniques which combine observations with a model. Bayes theorem has been employed as the foundation of many of these data assimilation methods (Liu and Gupta, 2007), simultaneously allowing for the calibration of hydrological models while accounting for prior knowledge of the system, and producing uncertainty estimates for parameter values, state variables, and model output. The Markov Chain Monte Carlo (MCMC) technique is one such data assimilation algorithm which has previously been applied to SRM (Panday et al., 2014). The MCMC Metropolis algorithm is utilized in this study for model calibration and assessing parameter uncertainty.
3.2 Study Area and Data 3.2.1 Study Area Description
The study region is the Upper Athabasca River Basin in the Albertan Rockies of Canada, roughly coterminous with Jasper National Park. Flow is simulated for the hydrometric station in Hinton, about 25 km downstream from the park boundary. The 9760 km2 watershed is characterized by
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sea level. The basin spans in latitude from 52°07’ N to 53°29’ N and in longitude from 117°06’ W to 119°04’ W. This region experiences a subarctic climate, with subfreezing mean daily
temperatures five months of the year at lower elevations and longer higher up. Coniferous forest covers much of the basin below 2200 m elevation, above which summer temperatures are insufficient to allow for tree growth. Glacier cover is about 3% of the watershed and is concentrated around the southern portion of the basin, including a portion of the Columbia Icefield.
